I can't seem to find the settings under the menu. I tried to find it under TCP/IP but to no avail.
I forgot to add that under IPv4 it says ARP Duplicate IP Address...
One possibility that people often don't think of, is handing out reserved DHCP/BootP addresses. Just add the MAC on your DHCP/BootP server and it will get everything from the server. No need to mess with every possible and different configuration on all the printers in your environment.
Also check the manual: http://www.manualslib.com/manual/72461/Hp-Cp3505.html?page=62#manual
If you go to Network Identification
tab, can't you set the hostname? What happens if you fill in a FQDN?
dnsmgmt.msc
and create printer A record, CNAME and PTR.